In this paper, applying two theorems of Ricceri and Bonanno, we will establish the existence of three weak solutions for a quasilinear elliptic system. Indeed, we will assign a differentiable nonlinear operator to a differential equation system such that the critical points of this operator are weak solutions of the system. In this paper, applying two theorems of R...

we consider the semilinear elliptic boundary value problem  = ∈∂ω− δ = ∈ωu x xu x f u x x( ) 0;( ) λ ( ( ));where λ > 0 is a parameter, ω is a bounded region in rn with a smooth boundary, and f is asmooth function. we prove, under some additional conditions, the existence of a positive solution for λlarge. we prove that our solution u for λ large is such that = →∞∈ω|| u ||: sup| u(x) |xas λ ...

by the mordell-weil theorem‎, ‎the group of rational points on an elliptic curve over a number field is a finitely generated abelian group‎. ‎there is no known algorithm for finding the rank of this group‎. ‎this paper computes the rank of the family $ e_p:y^2=x^3-3px $ of elliptic curves‎, ‎where p is a prime‎.

‎‎in the category of mordell curves (e_d:y^2=x^3+d) with nontrivial torsion groups we find curves of the generic rank two as quadratic twists of (e_1), ‎and of the generic rank at least two and at least three as cubic twists of (e_1). ‎previous work‎, ‎in the category of mordell curves with trivial torsion groups‎, ‎has found infinitely many elliptic curves with rank at least seven as sextic tw...

this paper is concerned with the following elliptic system:$$ left{ begin{array}{ll} -triangle u + b(x)nabla u + v(x)u=g(x, v), -triangle v - b(x)nabla v + v(x)v=f(x, u), end{array} right. $$ for $x in {r}^{n}$, where $v $, $b$ and $w$ are 1-periodic in $x$, and $f(x,t)$, $g(x,t)$ are super-quadratic. in this paper, we give a new technique to show the boundedness of cerami sequences and establi...

An amicable pair for an elliptic curve E/Q is a pair of primes (p, q) of good reduction for E satisfying #Ẽp(Fp) = q and #Ẽq(Fq) = p. In this paper we study elliptic amicable pairs and analogously defined longer elliptic aliquot cycles. We show that there exist elliptic curves with arbitrarily long aliqout cycles, but that CM elliptic curves (with j 6= 0) have no aliqout cycles of length greate...

in this paper, analysis of fluid flow and heat transfer over the bank of tubes is considered. k-ω sst model is applied for simulation of turbulent flow. in this paper, the improvement of efficiency of a bundle of circular tubes by changing the shape of the cross section of one row of the pipes to the elliptical cross section as an innovative plan is considered. as know, friction factor in turbu...

a modified model has been analytically developed to describe the induction time of an elliptic air bubble in contact with an elliptic hydrophobic oil droplet. the role of hydrophobicity was revealed in the slippage of liquid over the surfaces of bubble and droplet. in this condition, the analytical relationships for pressure distribution and consequently hydrodynamic resistance force through th...

advanced metering infrastructure (ami) is a key part of the smart grid; thus, one of the most important concerns is to offer a secure mutual authentication.  this study focuses on communication between a smart meter and a server on the utility side. hence, a mutual authentication mechanism in ami is presented based on the elliptic curve cryptography (ecc) and one time signature (ots) consists o...

Elliptic curves in Hesse form admit more suitable arithmetic than ones in Weierstrass form. But elliptic curve cryptosystems usually use Weierstrass form. It is known that both those forms are birationally equivalent. Birational equivalence is relatively hard to compute. We prove that elliptic curves in Hesse form and in Weierstrass form are linearly equivalent over initial field or its small e...